Say we have a two-alternative forced choice task on the basis of which we compute the four rates defined in signal detection theory, relating to hits, false alarms, correct rejections, and misses (HR, FAR, CRR, MR).

I know that the sensitivity index and the response bias are defined, respectively, as

d' = z(HR) - z(FAR)
c = -1/2 * [z(HR)+z(FAR)]

But I don't understand why the other two rates (the CRR and the MR) are not taken into consideration when defining either of these measures.

If someone constantly misses the signal, or fails to correctly reject it, shouldn't that somehow affect a measure of performance such as d'?

Is there any other SDT-based measure where the CRR and the MR are used?


1 Answer 1


The Miss Rate (MR) and Correct Rejection Rate (CRR) are already accounted for because they are functions of the Hit Rate (HR) and False Alarm Rate (FAR). Specifically:

MR = 1 - HR
CRR = 1 - FAR

So, for example, someone who misses the signal %90 of the time (MR=.9) will necessarily have HR = .1, and HR influences both sensitivity and response bias. Likewise, the CRR determines FAR, which also influences both estimates.


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